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Paper 3 2022 AQA Physics > Materials (RP 4) > Flashcards

Materials (RP 4) Flashcards

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1
Q

Are strain and stress on a material proportional?

A

Only up to the limit of proportionality.

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2
Q

What is the Young Modulus of a material?

A
  • The stress divided by the strain below the limit of proportionality.
  • Measure of stiffness.
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3
Q

What is the symbol for the Young modulus?

A

E

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4
Q

Give the equation for the Young modulus.

A

E = Stress / Strain

E = (F x L) / (A x ΔL)

Where:
F = Force (N)
A = Cross-sectional area (m²)
L = Original length (m)
ΔL = Extension (m)
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5
Q

Derive the equation for Young modulus.

A
  • E = Stress / Strain
  • E = (F / A) / (ΔL / L)
  • E = (F x L) / (A x ΔL)
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6
Q

What are the units for the Young modulus?

A

N/m² or Pa

Same as stress, since strain has no units.

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7
Q

What is Young modulus s measure of?

A

Stiffness of a material.

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8
Q

What is the Young modulus used for?

A

Engineers use it to ensure that materials they are using can withstand sufficient forces.

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9
Q

Describe an experiment to find the Young modulus of a wire.

A

1) Measure the diameter of a thin wire using a micrometer in several places and take an average.
2) Find the cross-sectional area of the wire using “A = πr²”.
3) Clamp the wire with a clamp at one end and over pulley at the other end, so that weights can be hung on the wire.
4) Align a ruler with the wire and attach a marker.
5) Start with the smallest weight to straighten the wire (but ignore this weight in calculations).
6) Measure the unstretched length of the wire from clamped end of the string to the marker.
7) Add 100g weights to the string and measure the extension.
8) Plot a stress (y) against strain (x) graph of your results. The gradient of the straight part is the Young modulus.

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10
Q

Name some ways in which the experiment to find the Young modulus of a wire is made more accurate.

A
  • Using a long, thin wire -> Reduces uncertainty
  • Taking several diameter readings and finding an average
  • Using a thin marker on the wire
  • Looking directly at the marker and ruler when measuring extension
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11
Q

Why is a stress-strain graph plotted, even though the stress is the independent variable?

A

On a stress-strain graph, the gradient gives the Young modulus.

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12
Q

How can you find the Young modulus from a stress-strain graph?

A
  • It is the gradient of the straight part of the line.

* This is because E = Stress / Strain

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13
Q

On a stress-strain graph, what does the area under the straight part of the line represent?

A
  • The strain energy stored per unit volume.

* i.e. The energy stored per 1m³ of wire

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14
Q

What are the units for elastic strain energy stored per unit volume?

A

J/m³

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15
Q

Why does the area under the straight part of the line on a stress-strain graph give the elastic energy stored in the wire?

A
  • Area = 1/2 x Stress x Strain
  • Area = 1/2 x N/m² x No units
  • Area = 1/2 x N/m²
  • Area = 1/2 x N x m / m³
  • Area = 1/2 x F x d / V
  • Area = 1/2 x Work done / Volume
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16
Q

What equation gives the elastic energy per unit volume of a stretched wire?

A

Energy per unit volume = 1/2 x Stress x Strain

As long as Hooke’s law is obeyed!

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17
Q

On a force-extension graph, what do the gradient and area under the line give?

A
  • Gradient = Spring constant (k)

* Area under line = Work done (or elastic energy stored)

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18
Q

On a stress-strain graph, what fit the gradient and area under the line give?

A
  • Gradient = Young modulus

* Area under line = Elastic energy stored per unit volume

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19
Q

On a force-extension and stress-strain graph, what do the gradient and area under the line give?

A

FORCE-EXTENSION:
• Gradient = Spring constant (k)
• Area under line = Work done (or elastic energy stored)
STRESS-STRAIN:
• Gradient = Young modulus
• Area under line = Elastic energy stored per unit volume

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20
Q

Describe a typical stress-strain graph for a DUCTILE material being stretched, with all the important points.

A
  • Straight line up until the limit of proportionality.
  • Curves towards the x-axis slightly until the elastic limit
  • Curves more towards the x-axis until the yield point
  • After yield point, the line goes down slightly
  • There may be a second peak before the breaking stress
  • The UTS is the highest stress reached, usually on the second peak
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21
Q

Do force-extension and stress-strain graphs show Hooke’s law?

A

Yes - straight lines through the origin on both show Hooke’s law.

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22
Q

If a material was stretched to the limit of proportionality, would it return to its original size and shape?

A

Yes, as long as the elastic limit is not exceeded.

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23
Q

What are the important points along a stress-strain graph?

A
  • Limit of proportionality (P)
  • Elastic limit (E)
  • Yield point (Y)
  • Ultimate tensile stress (UTS)
  • Breaking stress (B)
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24
Q

What is the yield point on a stress-strain graph?

A
  • The point beyond which the material starts to stretch without any extra load.
  • It is the stress at which a large amount of plastic deformation occurs with constant or reduced load
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25
Q

Describe the shape of a typical stress-strain graph for a ductile material.

A
  • Two peaks
  • Second peak is higher than the second
  • Goes through origin
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26
Q

Where is the limit of proportionality on a stress-strain graph?

A

Where the line starts curving.

27
Q

Where is the elastic limit on a stress-strain graph?

A

Soon after the limit of proportionality.

28
Q

Where is the yield point on a stress-strain graph?

A

When the line suddenly goes down (usually the peak of the first bump).

29
Q

On a stress-strain graph, which area represents the energy stored in the material per unit volume?

A

The area under the curve up to point P (the limit of proportionality).

30
Q

Do brittle materials obey Hooke’s law?

A

Yes

31
Q

Describe the stress-strain graph for a brittle material.

A
  • Straight line through origin.

* Reaches breaking point without curving.

32
Q

Give an example of a brittle material.

A

Ceramics (e.g. glass and pottery)

33
Q

What is the difference between a force-extension and stress-strain graph?

A
  • Force-extension is specific to the tested object and depends on the dimensions (metal wires of same material but different lengths and diameters produce different graphs)
  • Stress-strain describes the general behaviour of a material, because stress and strain are independent of dimensions
34
Q

What is the opposite of brittle?

A

Ductile

35
Q

Describe the loading-unloading force-extension graph for a metal wire stretched to below its elastic limit.

A

The loading and unloading lines are the same and both go through the origin.

36
Q

Describe the loading-unloading force-extension graph for a metal wire stretched beyond its elastic limit.

A
  • The loading line curves towards the x-axis until unloading starts.
  • The unloading line is parallel to the loading line and crosses the x-axis at a positive extension value.
37
Q

On a force-extension graph, why is the unloading line parallel to the loading line?

A

The stiffness constant (k) is still the same since the forces between the atoms are the same as they were during loading. Doesn’t cross (0,0) because it is permanently stretched.

38
Q

On a loading-unloading force-extension graph, how can you find the work done to deform the wire (i.e. the energy lost)?

A

It is the area between the two lines.

39
Q

What type of material will have two peaks on a stress-strain graph?

A

Ductile

40
Q

How can you tell this material is elastic

A

It returns to its original length after extension (0,0)

41
Q

For vertical spring which has a mass suspended vertically, what happens to the elastic strain energy when the end of the spring is with the mass is released from suspension?

A

Elastic Strain energy converts to kinetic energy (as the spring contracts) and gravitational potential energy (as the mass gains height).

The spring begins to compress and the kinetic energy is transferred back to stored elastic strain energy.

42
Q

For vertical spring which has a mass suspended vertically, then the mass is released from suspension, what is the overall energy changed summed up as?

A

Change in Kinetic energy = Change in Potential energy.

Potential energy includes gravitational potential and elastic strain energy.

43
Q

What do you need to remember for a lot of these rules and graphs

A

Hooke’s law limit of proportionality

The straight part of the graphs is what we usually talk about

44
Q

Will a material return to it’s original size and shape if it goes past it’s limit of proportionality?

A

Yes

45
Q

Will a material return to it’s original size and shape after it goes past it’s elastic limit?

A

no

46
Q

Describe the Force - Extension graph for a brittle material

A

Similar to stress - strain

47
Q

Describe the structure of brittle materials

A

Giant rigid structures.

Strong bonds = very stiff.

48
Q

What happens to a brittle material when stress is applied to it?
How does this differ to other materials?

A

Stress applied = any tiny cracks at the materials surface get bigger and bigger until the material breaks = BRITTLE FRACTURE.

Rigid structure = cracks grow.

Other materials aren’t brittle because the atoms within them move to prevent any cracks getting bigger.

49
Q

What does ductile mean?

A

A material that can undergo large plastic deformation before breaking and becomes elongated under tension

50
Q

Example of ductile materials?

A

Metals that can be drawn into wires such as copper.

Steel

51
Q

What is a tough material?

A

A material that can absorb lots of energy before it breaks

52
Q

What is a stiff material?

A

A material that resists extension while under tension

53
Q

What is a strong material?

A

Can withstand a large force without breaking

54
Q

What does brittle mean?

A

A material that doesn’t deform plastically before it fractures

55
Q

Example of strong materials?

A

Diamond, graphene

56
Q

Example of tough materials?

A

Steel, wood, rubber, rope

57
Q

Example of a stiff material

A

dimaond, steel, lead, wood

58
Q

What does a stress strain graph look like for brittle, ductile and polymeric materials?

A

Brittle: High UTS, low strain (doesn’t move much before it breaks)
Ductile: Curved after elastic limit (region of plastic deformation)
Polymeric: Small force (and stress) but long extension (and strain)

59
Q

What happens when two springs in parallel share the load?

A

The force on each spring is shared.
(If the spring constant is the same for each spring the force on each spring is halved.)

The extension on each spring is shared.
(If the spring constant is the same for each spring the extension on each spring is halved.)

Overall the spring constant (for both springs combined) will increase.
(If the spring constant is the same for each spring the overall spring constant increases.)

60
Q

What is the equation for the overall spring constant in parallel

A

k(T) = k(1) + k(2)

61
Q

What happens when two springs experience a force in series?

A

Both springs experience the same force.

Therefore they will both extend by the same amount.

Overall they will extend more.

If both springs are the same they will have an overall extension of 2x. x is extension of 1 wire.

Extends more so spring constant decreases

62
Q

What is the equation for total spring constant in series?

A

1/k(T) = 1/k(1) + 1/k(2)

63
Q

How do you remember the series and parallel equations for k?

A

Capacitors are the same as spring constant.

Resistance is opposite to spring constant

64
Q

What happens if you have two identical springs in parallel and 1 spring below in series experiencing a force?

A

Group the top springs together and think of them as 1 big spring : kT = k1 + k2 = 2k.
There are now two springs in series: use the equation:

Paper 3 2022 AQA Physics (3 decks)

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